A method of the kind mentioned in the opening paragraph and a device for carrying out this method are known from U.S. Pat. No. 3,543,979. In this known method, a crack initiation is provided in a side of a glass plate, whereupon a laser beam is moved along a desired line of rupture. By means of the laser beam, thermal energy is produced in the plate, which energy produces thermomechanical stresses, as a result of which, starting from the crack initiation, a crack is formed. The crack follows the laser beam at a certain distance along the desired line of rupture until the laser beam has reached an end of the line of rupture. Due to the thermomechanical stresses in the plate, the crack then propagates further to the end of the desired line of rupture. This method has the disadvantage that the speed at which the crack propagates through the plate is limited in that the energy is produced in a comparatively small part of the track. Further, the quantity of energy produced in the plate per unit time must not be excessively large because the plate then locally softens, melts or burns.
The speed at which the laser beam is moved over the plate and the energy is produced in the plate must not be excessively high because in this case insufficient stress is built up in the plate to cleave the plate, as a result of which the crack cannot follow the laser beam. Upon the start of the crack, the maximum admissible speed of the laser beam is lower than during the further formation of the crack. In the known method, the control of the power in relation to the speed of the laser beam upon the start of the crack from the crack initiation and during the further formation of the crack is comparatively complicated.